LMFDB - Embedded newform 585.2.dp.a.397.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(28,585)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("585.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.dp (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			397.3
Root			$0.493902i$ of defining polynomial
Character	$\chi$	$=$	585.397
Dual form			585.2.dp.a.28.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.427732 + 0.246951i) q^{2} +(-0.878030 - 1.52079i) q^{4} +(0.284413 + 2.21791i) q^{5} +(1.83775 + 3.18307i) q^{7} -1.85513i q^{8} +(-0.426062 + 1.01890i) q^{10} +(0.177987 + 0.664257i) q^{11} +(-2.92331 + 2.11051i) q^{13} +1.81533i q^{14} +(-1.29794 + 2.24809i) q^{16} +(-2.29359 - 0.614565i) q^{17} +(5.29067 + 1.41763i) q^{19} +(3.12325 - 2.37992i) q^{20} +(-0.0879082 + 0.328078i) q^{22} +(-1.30811 + 0.350507i) q^{23} +(-4.83822 + 1.26160i) q^{25} +(-1.77158 + 0.180816i) q^{26} +(3.22719 - 5.58966i) q^{28} +(8.24134 + 4.75814i) q^{29} +(4.81595 + 4.81595i) q^{31} +(-4.32351 + 2.49618i) q^{32} +(-0.829273 - 0.829273i) q^{34} +(-6.53707 + 4.98125i) q^{35} +(-0.917615 + 1.58936i) q^{37} +(1.91290 + 1.91290i) q^{38} +(4.11449 - 0.527621i) q^{40} +(0.534988 - 0.143350i) q^{41} +(-0.560778 + 2.09285i) q^{43} +(0.853919 - 0.853919i) q^{44} +(-0.646078 - 0.173116i) q^{46} +3.80918 q^{47} +(-3.25462 + 5.63717i) q^{49} +(-2.38101 - 0.655176i) q^{50} +(5.77640 + 2.59266i) q^{52} +(2.47293 - 2.47293i) q^{53} +(-1.42264 + 0.583682i) q^{55} +(5.90499 - 3.40925i) q^{56} +(2.35005 + 4.07041i) q^{58} +(2.69310 - 10.0508i) q^{59} +(-3.09904 - 5.36770i) q^{61} +(0.870630 + 3.24924i) q^{62} +2.72601 q^{64} +(-5.51234 - 5.88338i) q^{65} +(-10.6066 - 6.12371i) q^{67} +(1.07921 + 4.02768i) q^{68} +(-4.02624 + 0.516303i) q^{70} +(1.73500 - 6.47512i) q^{71} -3.37642i q^{73} +(-0.784986 + 0.453212i) q^{74} +(-2.48945 - 9.29074i) q^{76} +(-1.78728 + 1.78728i) q^{77} +3.12149i q^{79} +(-5.35521 - 2.23932i) q^{80} +(0.264231 + 0.0708006i) q^{82} -2.13918 q^{83} +(0.710723 - 5.26175i) q^{85} +(-0.756694 + 0.756694i) q^{86} +(1.23228 - 0.330188i) q^{88} +(-3.26255 + 0.874198i) q^{89} +(-12.0902 - 5.42653i) q^{91} +(1.68161 + 1.68161i) q^{92} +(1.62931 + 0.940681i) q^{94} +(-1.63944 + 12.1374i) q^{95} +(6.12606 - 3.53688i) q^{97} +(-2.78421 + 1.60746i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} + 6 q^{4} - 2 q^{7} - 2 q^{10} + 16 q^{11} - 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 16 q^{22} + 10 q^{23} + 18 q^{25} + 24 q^{26} + 18 q^{28} - 48 q^{32} + 2 q^{34} - 40 q^{35} - 4 q^{37}+ \cdots + 30 q^{98}+O(q^{100}) $ 20 * q + 6 * q^2 + 6 * q^4 - 2 * q^7 - 2 * q^10 + 16 * q^11 - 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 16 * q^22 + 10 * q^23 + 18 * q^25 + 24 * q^26 + 18 * q^28 - 48 * q^32 + 2 * q^34 - 40 * q^35 - 4 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 + 10 * q^43 + 36 * q^44 + 4 * q^46 + 40 * q^47 + 18 * q^49 - 36 * q^50 - 30 * q^52 + 10 * q^53 - 10 * q^55 + 16 * q^59 - 16 * q^61 + 44 * q^62 + 20 * q^64 + 14 * q^65 + 18 * q^67 - 22 * q^68 - 12 * q^70 + 16 * q^71 - 18 * q^74 - 64 * q^76 + 28 * q^77 + 2 * q^80 + 56 * q^82 - 48 * q^83 - 26 * q^85 - 60 * q^86 + 82 * q^88 + 6 * q^89 + 8 * q^91 + 8 * q^92 - 48 * q^94 + 26 * q^95 + 66 * q^97 + 30 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.427732	+	0.246951i	0.302452	+	0.174621i	0.643544	−	0.765409i	$-0.277463\pi$
$2$	0.427732	+	0.246951i	0.302452	+	0.174621i	−0.341092	+	0.940030i	$0.610797\pi$
$3$		0			0
$3$		0			0
$4$	−0.878030	−	1.52079i	−0.439015	−	0.760397i
$5$	0.284413	+	2.21791i	0.127193	+	0.991878i
$5$	0.284413	+	2.21791i	0.127193	+	0.991878i
$6$		0			0
$7$	1.83775	+	3.18307i	0.694603	+	1.20309i	0.970314	+	0.241847i	$0.0777532\pi$
$7$	1.83775	+	3.18307i	0.694603	+	1.20309i	−0.275712	+	0.961240i	$0.588914\pi$
$8$		−	1.85513i		−	0.655886i
$9$		0			0
$10$	−0.426062	+	1.01890i	−0.134733	+	0.322206i
$11$	0.177987	+	0.664257i	0.0536651	+	0.200281i	0.987553	−	0.157284i	$-0.0502738\pi$
$11$	0.177987	+	0.664257i	0.0536651	+	0.200281i	−0.933888	+	0.357565i	$0.883607\pi$
$12$		0			0
$13$	−2.92331	+	2.11051i	−0.810781	+	0.585350i
$13$	−2.92331	+	2.11051i	−0.810781	+	0.585350i
$14$			1.81533i			0.485168i
$15$		0			0
$16$	−1.29794	+	2.24809i	−0.324484	+	0.562023i
$17$	−2.29359	−	0.614565i	−0.556277	−	0.149054i	−0.0302815	−	0.999541i	$-0.509640\pi$
$17$	−2.29359	−	0.614565i	−0.556277	−	0.149054i	−0.525995	+	0.850487i	$0.676307\pi$
$18$		0			0
$19$	5.29067	+	1.41763i	1.21376	+	0.325227i	0.808238	−	0.588857i	$-0.200422\pi$
$19$	5.29067	+	1.41763i	1.21376	+	0.325227i	0.405526	+	0.914084i	$0.367088\pi$
$20$	3.12325	−	2.37992i	0.698381	−	0.532167i
$21$		0			0
$22$	−0.0879082	+	0.328078i	−0.0187421	+	0.0699464i
$23$	−1.30811	+	0.350507i	−0.272760	+	0.0730858i	−0.392606	−	0.919707i	$-0.628426\pi$
$23$	−1.30811	+	0.350507i	−0.272760	+	0.0730858i	0.119846	+	0.992792i	$0.461760\pi$
$24$		0			0
$25$	−4.83822	+	1.26160i	−0.967644	+	0.252320i
$26$	−1.77158	+	0.180816i	−0.347436	+	0.0354610i
$27$		0			0
$28$	3.22719	−	5.58966i	0.609882	−	1.05635i
$29$	8.24134	+	4.75814i	1.53038	+	0.883564i	0.999344	+	0.0362142i	$0.0115299\pi$
$29$	8.24134	+	4.75814i	1.53038	+	0.883564i	0.531034	+	0.847350i	$0.321803\pi$
$30$		0			0
$31$	4.81595	+	4.81595i	0.864970	+	0.864970i	0.991910	−	0.126940i	$-0.0405157\pi$
$31$	4.81595	+	4.81595i	0.864970	+	0.864970i	−0.126940	+	0.991910i	$0.540516\pi$
$32$	−4.32351	+	2.49618i	−0.764295	+	0.441266i
$33$		0			0
$34$	−0.829273	−	0.829273i	−0.142219	−	0.142219i
$35$	−6.53707	+	4.98125i	−1.10497	+	0.841986i
$36$		0			0
$37$	−0.917615	+	1.58936i	−0.150855	+	0.261289i	−0.931542	−	0.363634i	$-0.881536\pi$
$37$	−0.917615	+	1.58936i	−0.150855	+	0.261289i	0.780687	+	0.624922i	$0.214869\pi$
$38$	1.91290	+	1.91290i	0.310314	+	0.310314i
$39$		0			0
$40$	4.11449	−	0.527621i	0.650559	−	0.0834242i
$41$	0.534988	−	0.143350i	0.0835510	−	0.0223874i	−0.216801	−	0.976216i	$-0.569562\pi$
$41$	0.534988	−	0.143350i	0.0835510	−	0.0223874i	0.300352	+	0.953828i	$0.402896\pi$
$42$		0			0
$43$	−0.560778	+	2.09285i	−0.0855178	+	0.319157i	−0.995412	−	0.0956841i	$-0.969496\pi$
$43$	−0.560778	+	2.09285i	−0.0855178	+	0.319157i	0.909894	+	0.414841i	$0.136163\pi$
$44$	0.853919	−	0.853919i	0.128733	−	0.128733i
$45$		0			0
$46$	−0.646078	−	0.173116i	−0.0952590	−	0.0255246i
$47$	3.80918			0.555626			0.277813	−	0.960635i	$-0.410390\pi$
$47$	3.80918			0.555626			0.277813	+	0.960635i	$0.410390\pi$
$48$		0			0
$49$	−3.25462	+	5.63717i	−0.464946	+	0.805310i
$50$	−2.38101	−	0.655176i	−0.336726	−	0.0926559i
$51$		0			0
$52$	5.77640	+	2.59266i	0.801043	+	0.359538i
$53$	2.47293	−	2.47293i	0.339683	−	0.339683i	−0.516565	−	0.856248i	$-0.672789\pi$
$53$	2.47293	−	2.47293i	0.339683	−	0.339683i	0.856248	+	0.516565i	$0.172789\pi$
$54$		0			0
$55$	−1.42264	+	0.583682i	−0.191828	+	0.0787036i
$56$	5.90499	−	3.40925i	0.789088	−	0.455580i
$57$		0			0
$58$	2.35005	+	4.07041i	0.308577	+	0.534471i
$59$	2.69310	−	10.0508i	0.350612	−	1.30850i	−0.535305	−	0.844659i	$-0.679803\pi$
$59$	2.69310	−	10.0508i	0.350612	−	1.30850i	0.885917	−	0.463844i	$-0.153530\pi$
$60$		0			0
$61$	−3.09904	−	5.36770i	−0.396792	−	0.687263i	0.596536	−	0.802586i	$-0.296543\pi$
$61$	−3.09904	−	5.36770i	−0.396792	−	0.687263i	−0.993328	+	0.115323i	$0.963210\pi$
$62$	0.870630	+	3.24924i	0.110570	+	0.412653i
$63$		0			0
$64$	2.72601			0.340751
$65$	−5.51234	−	5.88338i	−0.683721	−	0.729743i
$66$		0			0
$67$	−10.6066	−	6.12371i	−1.29580	−	0.748130i	−0.316124	−	0.948718i	$-0.602381\pi$
$67$	−10.6066	−	6.12371i	−1.29580	−	0.748130i	−0.979676	+	0.200588i	$0.935715\pi$
$68$	1.07921	+	4.02768i	0.130874	+	0.488428i
$69$		0			0
$70$	−4.02624	+	0.516303i	−0.481227	+	0.0617101i
$71$	1.73500	−	6.47512i	0.205907	−	0.768456i	−0.783264	−	0.621689i	$-0.786447\pi$
$71$	1.73500	−	6.47512i	0.205907	−	0.768456i	0.989171	−	0.146767i	$-0.0468866\pi$
$72$		0			0
$73$		−	3.37642i		−	0.395180i	−0.980285	−	0.197590i	$-0.936688\pi$
$73$		−	3.37642i		−	0.395180i	0.980285	−	0.197590i	$-0.0633115\pi$
$74$	−0.784986	+	0.453212i	−0.0912528	+	0.0526848i
$75$		0			0
$76$	−2.48945	−	9.29074i	−0.285559	−	1.06572i
$77$	−1.78728	+	1.78728i	−0.203680	+	0.203680i
$78$		0			0
$79$			3.12149i			0.351195i	0.984462	+	0.175598i	$0.0561857\pi$
$79$			3.12149i			0.351195i	−0.984462	+	0.175598i	$0.943814\pi$
$80$	−5.35521	−	2.23932i	−0.598730	−	0.250363i
$81$		0			0
$82$	0.264231	+	0.0708006i	0.0291795	+	0.00781862i
$83$	−2.13918			−0.234805			−0.117403	−	0.993084i	$-0.537457\pi$
$83$	−2.13918			−0.234805			−0.117403	+	0.993084i	$0.537457\pi$
$84$		0			0
$85$	0.710723	−	5.26175i	0.0770887	−	0.570717i
$86$	−0.756694	+	0.756694i	−0.0815964	+	0.0815964i
$87$		0			0
$88$	1.23228	−	0.330188i	0.131361	−	0.0351982i
$89$	−3.26255	+	0.874198i	−0.345830	+	0.0926648i	−0.427553	−	0.903990i	$-0.640624\pi$
$89$	−3.26255	+	0.874198i	−0.345830	+	0.0926648i	0.0817233	+	0.996655i	$0.473958\pi$
$90$		0			0
$91$	−12.0902	−	5.42653i	−1.26740	−	0.568855i
$92$	1.68161	+	1.68161i	0.175320	+	0.175320i
$93$		0			0
$94$	1.62931	+	0.940681i	0.168050	+	0.0970238i
$95$	−1.63944	+	12.1374i	−0.168203	+	1.24527i
$96$		0			0
$97$	6.12606	−	3.53688i	0.622007	−	0.359116i	−0.155643	−	0.987813i	$-0.549745\pi$
$97$	6.12606	−	3.53688i	0.622007	−	0.359116i	0.777650	+	0.628697i	$0.216412\pi$
$98$	−2.78421	+	1.60746i	−0.281248	+	0.162378i
$99$		0			0
$100$	6.16674	+	6.25021i	0.616674	+	0.625021i
$101$	−12.9641	−	7.48483i	−1.28998	−	0.744769i	−0.311327	−	0.950303i	$-0.600774\pi$
$101$	−12.9641	−	7.48483i	−1.28998	−	0.744769i	−0.978650	+	0.205534i	$0.934107\pi$
$102$		0			0
$103$	−3.17851	−	3.17851i	−0.313188	−	0.313188i	0.532956	−	0.846143i	$-0.321081\pi$
$103$	−3.17851	−	3.17851i	−0.313188	−	0.313188i	−0.846143	+	0.532956i	$0.821081\pi$
$104$	3.91526	+	5.42311i	0.383923	+	0.531780i
$105$		0			0
$106$	1.66844	−	0.447058i	0.162054	−	0.0434221i
$107$	−14.7329	+	3.94767i	−1.42428	+	0.381635i	−0.887001	−	0.461767i	$-0.847216\pi$
$107$	−14.7329	+	3.94767i	−1.42428	+	0.381635i	−0.537282	+	0.843403i	$0.680549\pi$
$108$		0			0
$109$	2.25902	−	2.25902i	0.216375	−	0.216375i	−0.590594	−	0.806969i	$-0.701107\pi$
$109$	2.25902	−	2.25902i	0.216375	−	0.216375i	0.806969	+	0.590594i	$0.201107\pi$
$110$	−0.752648	−	0.101663i	−0.0717622	−	0.00969315i
$111$		0			0
$112$	−9.54111			−0.901550
$113$	16.0061	+	4.28882i	1.50573	+	0.403458i	0.915014	−	0.403423i	$-0.132180\pi$
$113$	16.0061	+	4.28882i	1.50573	+	0.403458i	0.590713	+	0.806881i	$0.298846\pi$
$114$		0			0
$115$	−1.14944	−	2.80158i	−0.107185	−	0.261248i
$116$		−	16.7112i		−	1.55159i
$117$		0			0
$118$	3.63398	−	3.63398i	0.334535	−	0.334535i
$119$	−2.25883	−	8.43007i	−0.207067	−	0.772783i
$120$		0			0
$121$	9.11672	−	5.26354i	0.828793	−	0.478504i
$122$		−	3.06124i		−	0.277152i
$123$		0			0
$124$	3.09551	−	11.5526i	0.277985	−	1.03746i
$125$	−4.17416	−	10.3719i	−0.373349	−	0.927691i
$126$		0			0
$127$	−2.14812	−	8.01688i	−0.190614	−	0.711383i	−0.993359	−	0.115059i	$-0.963294\pi$
$127$	−2.14812	−	8.01688i	−0.190614	−	0.711383i	0.802744	−	0.596324i	$-0.203372\pi$
$128$	9.81302	+	5.66555i	0.867356	+	0.500768i
$129$		0			0
$130$	−0.904895	−	3.87778i	−0.0793645	−	0.340104i
$131$	−1.37409			−0.120054			−0.0600272	−	0.998197i	$-0.519119\pi$
$131$	−1.37409			−0.120054			−0.0600272	+	0.998197i	$0.519119\pi$
$132$		0			0
$133$	5.21049	+	19.4458i	0.451807	+	1.68617i
$134$	−3.02451	−	5.23861i	−0.261278	−	0.452547i
$135$		0			0
$136$	−1.14010	+	4.25489i	−0.0977624	+	0.364854i
$137$	6.16380	+	10.6760i	0.526609	+	0.912114i	0.999519	+	0.0310029i	$0.00987013\pi$
$137$	6.16380	+	10.6760i	0.526609	+	0.912114i	−0.472910	+	0.881111i	$0.656797\pi$
$138$		0			0
$139$	5.54392	−	3.20078i	0.470229	−	0.271487i	−0.246107	−	0.969243i	$-0.579151\pi$
$139$	5.54392	−	3.20078i	0.470229	−	0.271487i	0.716336	+	0.697756i	$0.245818\pi$
$140$	13.3152	+	5.56784i	1.12534	+	0.470569i
$141$		0			0
$142$	2.34115	−	2.34115i	0.196465	−	0.196465i
$143$	−1.92223	−	1.56619i	−0.160745	−	0.130971i
$144$		0			0
$145$	−8.20917	+	19.6318i	−0.681734	+	1.63033i
$146$	0.833811	−	1.44420i	0.0690067	−	0.119523i
$147$		0			0
$148$	3.22278			0.264911
$149$	16.2300	+	4.34882i	1.32961	+	0.356269i	0.852571	−	0.522611i	$-0.175042\pi$
$149$	16.2300	+	4.34882i	1.32961	+	0.356269i	0.477043	+	0.878880i	$0.341709\pi$
$150$		0			0
$151$	−3.31542	+	3.31542i	−0.269805	+	0.269805i	−0.829022	−	0.559217i	$-0.811102\pi$
$151$	−3.31542	+	3.31542i	−0.269805	+	0.269805i	0.559217	+	0.829022i	$0.311102\pi$
$152$	2.62988	−	9.81486i	0.213312	−	0.796090i
$153$		0			0
$154$	−1.20585	+	0.323106i	−0.0971699	+	0.0260366i
$155$	−9.31161	+	12.0510i	−0.747926	+	0.967963i
$156$		0			0
$157$	9.87941	+	9.87941i	0.788463	+	0.788463i	0.981242	−	0.192779i	$-0.0617501\pi$
$157$	9.87941	+	9.87941i	0.788463	+	0.788463i	−0.192779	+	0.981242i	$0.561750\pi$
$158$	−0.770855	+	1.33516i	−0.0613259	+	0.106220i
$159$		0			0
$160$	−6.76595	−	8.87919i	−0.534895	−	0.701962i
$161$	−3.51966	−	3.51966i	−0.277388	−	0.277388i
$162$		0			0
$163$	−0.114289	+	0.0659848i	−0.00895180	+	0.00516833i	−0.504469	−	0.863430i	$-0.668312\pi$
$163$	−0.114289	+	0.0659848i	−0.00895180	+	0.00516833i	0.495517	+	0.868598i	$0.334978\pi$
$164$	−0.687741	−	0.687741i	−0.0537035	−	0.0537035i
$165$		0			0
$166$	−0.914995	−	0.528272i	−0.0710174	−	0.0410019i
$167$	10.8184	−	18.7380i	0.837152	−	1.44999i	−0.0551149	−	0.998480i	$-0.517553\pi$
$167$	10.8184	−	18.7380i	0.837152	−	1.44999i	0.892267	−	0.451509i	$-0.149114\pi$
$168$		0			0
$169$	4.09151	−	12.3393i	0.314731	−	0.949181i
$170$	1.60339	−	2.07510i	0.122975	−	0.159153i
$171$		0			0
$172$	3.67518	−	0.984760i	0.280230	−	0.0750873i
$173$	2.00162	−	7.47013i	0.152180	−	0.567943i	−0.847150	−	0.531353i	$-0.821684\pi$
$173$	2.00162	−	7.47013i	0.152180	−	0.567943i	0.999330	−	0.0365902i	$-0.0116496\pi$
$174$		0			0
$175$	−12.9072	−	13.0819i	−0.975691	−	0.988898i
$176$	−1.72433	−	0.462032i	−0.129976	−	0.0348270i
$177$		0			0
$178$	−1.61138	−	0.431768i	−0.120778	−	0.0323624i
$179$	−8.17681	+	14.1627i	−0.611164	+	1.05857i	0.379881	+	0.925035i	$0.375965\pi$
$179$	−8.17681	+	14.1627i	−0.611164	+	1.05857i	−0.991045	+	0.133531i	$0.957368\pi$
$180$		0			0
$181$		−	18.0387i		−	1.34081i	−0.741997	−	0.670403i	$-0.766121\pi$
$181$		−	18.0387i		−	1.34081i	0.741997	−	0.670403i	$-0.233879\pi$
$182$	−3.83127	−	5.30678i	−0.283993	−	0.393365i
$183$		0			0
$184$	0.650235	+	2.42671i	0.0479359	+	0.178899i
$185$	−3.78603	−	1.58315i	−0.278354	−	0.116396i
$186$		0			0
$187$		−	1.63292i		−	0.119411i
$188$	−3.34458	−	5.79298i	−0.243928	−	0.422496i
$189$		0			0
$190$	−3.69858	+	4.78669i	−0.268324	+	0.347263i
$191$	2.59552	+	4.49557i	0.187805	+	0.325288i	0.944518	−	0.328459i	$-0.106529\pi$
$191$	2.59552	+	4.49557i	0.187805	+	0.325288i	−0.756713	+	0.653747i	$0.773196\pi$
$192$		0			0
$193$	−8.74813	−	5.05073i	−0.629704	−	0.363560i	0.150934	−	0.988544i	$-0.451772\pi$
$193$	−8.74813	−	5.05073i	−0.629704	−	0.363560i	−0.780637	+	0.624984i	$0.785105\pi$
$194$	3.49375			0.250836
$195$		0			0
$196$	11.4306			0.816473
$197$	11.3137	+	6.53197i	0.806068	+	0.465384i	0.845589	−	0.533835i	$-0.179250\pi$
$197$	11.3137	+	6.53197i	0.806068	+	0.465384i	−0.0395205	+	0.999219i	$0.512583\pi$
$198$		0			0
$199$	−3.92506	−	6.79840i	−0.278240	−	0.481926i	0.692707	−	0.721219i	$-0.256418\pi$
$199$	−3.92506	−	6.79840i	−0.278240	−	0.481926i	−0.970947	+	0.239293i	$0.923084\pi$
$200$	2.34043	+	8.97550i	0.165493	+	0.634664i
$201$		0			0
$202$	−3.69677	−	6.40300i	−0.260104	−	0.450513i
$203$			34.9770i			2.45491i
$204$		0			0
$205$	0.470093	+	1.14578i	0.0328327	+	0.0800249i
$206$	−0.574613	−	2.14448i	−0.0400352	−	0.149413i
$207$		0			0
$208$	−0.950343	−	9.31118i	−0.0658944	−	0.645614i
$209$			3.76669i			0.260547i
$210$		0			0
$211$	−6.21205	+	10.7596i	−0.427655	+	0.740720i	−0.996664	−	0.0816108i	$-0.973994\pi$
$211$	−6.21205	+	10.7596i	−0.427655	+	0.740720i	0.569009	+	0.822331i	$0.307327\pi$
$212$	−5.93213	−	1.58951i	−0.407420	−	0.109168i
$213$		0			0
$214$	−7.27661	−	1.94976i	−0.497419	−	0.133283i
$215$	−4.80124	−	0.648520i	−0.327442	−	0.0442287i
$216$		0			0
$217$	−6.47901	+	24.1800i	−0.439824	+	1.64145i
$218$	1.52412	−	0.408387i	0.103226	−	0.0276594i
$219$		0			0
$220$	2.13678	+	1.65105i	0.144062	+	0.111314i
$221$	8.00192	−	3.04407i	0.538267	−	0.204766i
$222$		0			0
$223$	−4.97247	+	8.61258i	−0.332981	+	0.576741i	−0.983095	−	0.183096i	$-0.941388\pi$
$223$	−4.97247	+	8.61258i	−0.332981	+	0.576741i	0.650114	+	0.759837i	$0.274721\pi$
$224$	−15.8910	−	9.17468i	−1.06176	−	0.613009i
$225$		0			0
$226$	5.78718	+	5.78718i	0.384958	+	0.384958i
$227$	−12.6490	+	7.30290i	−0.839543	+	0.484710i	−0.857109	−	0.515135i	$-0.827742\pi$
$227$	−12.6490	+	7.30290i	−0.839543	+	0.484710i	0.0175659	+	0.999846i	$0.494408\pi$
$228$		0			0
$229$	15.6183	+	15.6183i	1.03209	+	1.03209i	0.999468	+	0.0326207i	$0.0103853\pi$
$229$	15.6183	+	15.6183i	1.03209	+	1.03209i	0.0326207	+	0.999468i	$0.489615\pi$
$230$	0.200203	−	1.48218i	0.0132010	−	0.0977319i
$231$		0			0
$232$	8.82695	−	15.2887i	0.579517	−	1.00375i
$233$	−16.5625	−	16.5625i	−1.08505	−	1.08505i	−0.996030	−	0.0890148i	$-0.971628\pi$
$233$	−16.5625	−	16.5625i	−1.08505	−	1.08505i	−0.0890148	−	0.996030i	$-0.528372\pi$
$234$		0			0
$235$	1.08338	+	8.44841i	0.0706719	+	0.551113i
$236$	−17.6498	+	4.72926i	−1.14891	+	0.307848i
$237$		0			0
$238$	1.11564	−	4.16362i	0.0723162	−	0.269888i
$239$	14.6022	−	14.6022i	0.944535	−	0.944535i	−0.0540053	−	0.998541i	$-0.517199\pi$
$239$	14.6022	−	14.6022i	0.944535	−	0.944535i	0.998541	+	0.0540053i	$0.0171988\pi$
$240$		0			0
$241$	2.99335	+	0.802065i	0.192818	+	0.0516656i	0.353936	−	0.935270i	$-0.384843\pi$
$241$	2.99335	+	0.802065i	0.192818	+	0.0516656i	−0.161117	+	0.986935i	$0.551510\pi$
$242$	5.19935			0.334227
$243$		0			0
$244$	−5.44211	+	9.42600i	−0.348395	+	0.603438i
$245$	−13.4284	−	5.61516i	−0.857907	−	0.358740i
$246$		0			0
$247$	−18.4582	+	7.02183i	−1.17447	+	0.446788i
$248$	8.93419	−	8.93419i	0.567322	−	0.567322i
$249$		0			0
$250$	0.775929	−	5.46720i	0.0490741	−	0.345776i
$251$	25.5728	−	14.7645i	1.61414	−	0.931925i	0.625745	−	0.780028i	$-0.284795\pi$
$251$	25.5728	−	14.7645i	1.61414	−	0.931925i	0.988396	−	0.151897i	$-0.0485382\pi$
$252$		0			0
$253$	−0.465654	−	0.806536i	−0.0292754	−	0.0507065i
$254$	1.06096	−	3.95955i	0.0665704	−	0.248444i
$255$		0			0
$256$	0.0722145	+	0.125079i	0.00451341	+	0.00781745i
$257$	1.85447	+	6.92097i	0.115679	+	0.431718i	0.999337	−	0.0364143i	$-0.0115936\pi$
$257$	1.85447	+	6.92097i	0.115679	+	0.431718i	−0.883658	+	0.468133i	$0.844927\pi$
$258$		0			0
$259$	−6.74538			−0.419137
$260$	−4.10740	+	13.5489i	−0.254730	+	0.840268i
$261$		0			0
$262$	−0.587740	−	0.339332i	−0.0363107	−	0.0209640i
$263$	3.48511	+	13.0066i	0.214901	+	0.802023i	0.986201	+	0.165551i	$0.0529402\pi$
$263$	3.48511	+	13.0066i	0.214901	+	0.802023i	−0.771300	+	0.636472i	$0.780393\pi$
$264$		0			0
$265$	6.18807	+	4.78140i	0.380130	+	0.293719i
$266$	−2.57347	+	9.60433i	−0.157790	+	0.588879i
$267$		0			0
$268$			21.5072i			1.31376i
$269$	7.01806	−	4.05188i	0.427899	−	0.247047i	−0.270552	−	0.962705i	$-0.587206\pi$
$269$	7.01806	−	4.05188i	0.427899	−	0.247047i	0.698451	+	0.715658i	$0.253873\pi$
$270$		0			0
$271$	−2.38026	−	8.88325i	−0.144590	−	0.539619i	−0.999773	−	0.0212923i	$-0.993222\pi$
$271$	−2.38026	−	8.88325i	−0.144590	−	0.539619i	0.855183	−	0.518326i	$-0.173445\pi$
$272$	4.35853	−	4.35853i	0.264275	−	0.264275i
$273$		0			0
$274$			6.08862i			0.367827i
$275$	−1.69917	−	2.98927i	−0.102464	−	0.180260i
$276$		0			0
$277$	24.9641	+	6.68911i	1.49995	+	0.401910i	0.913082	−	0.407775i	$-0.133695\pi$
$277$	24.9641	+	6.68911i	1.49995	+	0.401910i	0.586865	+	0.809685i	$0.300362\pi$
$278$	3.16174			0.189629
$279$		0			0
$280$	9.24085	+	12.1271i	0.552246	+	0.724732i
$281$	−5.41928	+	5.41928i	−0.323287	+	0.323287i	−0.850027	−	0.526740i	$-0.823414\pi$
$281$	−5.41928	+	5.41928i	−0.323287	+	0.323287i	0.526740	+	0.850027i	$0.323414\pi$
$282$		0			0
$283$	8.48623	−	2.27388i	0.504454	−	0.135168i	0.00238762	−	0.999997i	$-0.499240\pi$
$283$	8.48623	−	2.27388i	0.504454	−	0.135168i	0.502066	+	0.864829i	$0.332573\pi$
$284$	−11.3707	+	3.04677i	−0.674728	+	0.180793i
$285$		0			0
$286$	−0.435428	−	1.14460i	−0.0257474	−	0.0676819i
$287$	1.43946	+	1.43946i	0.0849688	+	0.0849688i
$288$		0			0
$289$	−9.83958	−	5.68088i	−0.578799	−	0.334170i
$290$	−8.35941	+	6.36988i	−0.490882	+	0.374052i
$291$		0			0
$292$	−5.13484	+	2.96460i	−0.300494	+	0.173490i
$293$	−11.4627	+	6.61798i	−0.669657	+	0.386626i	−0.795947	−	0.605367i	$-0.793026\pi$
$293$	−11.4627	+	6.61798i	−0.669657	+	0.386626i	0.126290	+	0.991993i	$0.459693\pi$
$294$		0			0
$295$	23.0577	+	3.11448i	1.34247	+	0.181332i
$296$	2.94846	+	1.70229i	0.171375	+	0.0989437i
$297$		0			0
$298$	5.86814	+	5.86814i	0.339932	+	0.339932i
$299$	3.08427	−	3.78542i	0.178368	−	0.218916i
$300$		0			0
$301$	−7.69226	+	2.06114i	−0.443375	+	0.118802i
$302$	−2.23685	+	0.599363i	−0.128716	+	0.0344895i
$303$		0			0
$304$	−10.0539	+	10.0539i	−0.576632	+	0.576632i
$305$	11.0236	−	8.40003i	0.631212	−	0.480984i
$306$		0			0
$307$	−15.4782			−0.883389			−0.441695	−	0.897165i	$-0.645623\pi$
$307$	−15.4782			−0.883389			−0.441695	+	0.897165i	$0.645623\pi$
$308$	4.28737	+	1.14880i	0.244296	+	0.0654588i
$309$		0			0
$310$	−6.95889	+	2.85510i	−0.395238	+	0.162159i
$311$			5.34922i			0.303326i	0.988432	+	0.151663i	$0.0484629\pi$
$311$			5.34922i			0.303326i	−0.988432	+	0.151663i	$0.951537\pi$
$312$		0			0
$313$	24.3923	−	24.3923i	1.37873	−	1.37873i	0.531967	−	0.846765i	$-0.321453\pi$
$313$	24.3923	−	24.3923i	1.37873	−	1.37873i	0.846765	−	0.531967i	$-0.178547\pi$
$314$	1.78601	+	6.66547i	0.100790	+	0.376154i
$315$		0			0
$316$	4.74714	−	2.74076i	0.267048	−	0.154180i
$317$			18.9851i			1.06631i	0.846017	+	0.533156i	$0.178994\pi$
$317$			18.9851i			1.06631i	−0.846017	+	0.533156i	$0.821006\pi$
$318$		0			0
$319$	−1.69378	+	6.32125i	−0.0948332	+	0.353922i
$320$	0.775312	+	6.04604i	0.0433412	+	0.337984i
$321$		0			0
$322$	−0.636287	−	2.37466i	−0.0354589	−	0.132334i
$323$	−11.2634	−	6.50293i	−0.626712	−	0.361832i
$324$		0			0
$325$	11.4810	−	13.8992i	0.636852	−	0.770986i
$326$	−0.0651800			−0.00360999
$327$		0			0
$328$	−0.265931	−	0.992469i	−0.0146836	−	0.0548000i
$329$	7.00031	+	12.1249i	0.385940	+	0.668467i
$330$		0			0
$331$	−1.81607	+	6.77766i	−0.0998202	+	0.372534i	−0.997706	−	0.0676941i	$-0.978436\pi$
$331$	−1.81607	+	6.77766i	−0.0998202	+	0.372534i	0.897886	+	0.440228i	$0.145102\pi$
$332$	1.87826	+	3.25325i	0.103083	+	0.178545i
$333$		0			0
$334$	9.25473	−	5.34322i	0.506396	−	0.292368i
$335$	10.5652	−	25.2661i	0.577237	−	1.38043i
$336$		0			0
$337$	−1.10195	+	1.10195i	−0.0600271	+	0.0600271i	−0.736483	−	0.676456i	$-0.763515\pi$
$337$	−1.10195	+	1.10195i	−0.0600271	+	0.0600271i	0.676456	+	0.736483i	$0.263515\pi$
$338$	4.79728	−	4.26753i	0.260938	−	0.232123i
$339$		0			0
$340$	−8.62608	+	3.53912i	−0.467815	+	0.191936i
$341$	−2.34185	+	4.05620i	−0.126818	+	0.219656i
$342$		0			0
$343$	1.80378			0.0973947
$344$	3.88250	+	1.04031i	0.209331	+	0.0560899i
$345$		0			0
$346$	2.70091	−	2.70091i	0.145202	−	0.145202i
$347$	−6.68561	+	24.9510i	−0.358902	+	1.33944i	0.516600	+	0.856227i	$0.327197\pi$
$347$	−6.68561	+	24.9510i	−0.358902	+	1.33944i	−0.875502	+	0.483214i	$0.839469\pi$
$348$		0			0
$349$	−9.07958	+	2.43287i	−0.486019	+	0.130228i	−0.493504	−	0.869744i	$-0.664284\pi$
$349$	−9.07958	+	2.43287i	−0.486019	+	0.130228i	0.00748510	+	0.999972i	$0.497617\pi$
$350$	−2.29023	−	8.78298i	−0.122418	−	0.469470i
$351$		0			0
$352$	−2.42763	−	2.42763i	−0.129393	−	0.129393i
$353$	−1.63274	+	2.82798i	−0.0869017	+	0.150518i	−0.906200	−	0.422849i	$-0.861030\pi$
$353$	−1.63274	+	2.82798i	−0.0869017	+	0.150518i	0.819298	+	0.573368i	$0.194363\pi$
$354$		0			0
$355$	14.8547	+	2.00647i	0.788404	+	0.106492i
$356$	4.19410	+	4.19410i	0.222287	+	0.222287i
$357$		0			0
$358$	−6.99496	+	4.03854i	−0.369695	+	0.213444i
$359$	−3.12090	−	3.12090i	−0.164715	−	0.164715i	0.619937	−	0.784652i	$-0.287158\pi$
$359$	−3.12090	−	3.12090i	−0.164715	−	0.164715i	−0.784652	+	0.619937i	$0.787158\pi$
$360$		0			0
$361$	9.52706	+	5.50045i	0.501424	+	0.289497i
$362$	4.45468	−	7.71573i	0.234133	−	0.405530i
$363$		0			0
$364$	2.36294	+	23.1514i	0.123852	+	1.21346i
$365$	7.48859	−	0.960297i	0.391971	−	0.0502643i
$366$		0			0
$367$	−24.2349	+	6.49371i	−1.26505	+	0.338969i	−0.828132	−	0.560533i	$-0.810596\pi$
$367$	−24.2349	+	6.49371i	−1.26505	+	0.338969i	−0.436917	+	0.899502i	$0.643930\pi$
$368$	0.909872	−	3.39569i	0.0474303	−	0.177012i
$369$		0			0
$370$	−1.22844	−	1.61213i	−0.0638636	−	0.0838105i
$371$	12.4161	+	3.32690i	0.644614	+	0.172724i
$372$		0			0
$373$	11.0372	+	2.95740i	0.571483	+	0.153128i	0.532976	−	0.846130i	$-0.321073\pi$
$373$	11.0372	+	2.95740i	0.571483	+	0.153128i	0.0385061	+	0.999258i	$0.487740\pi$
$374$	0.403250	−	0.698450i	0.0208516	−	0.0361160i
$375$		0			0
$376$		−	7.06651i		−	0.364427i
$377$	−34.1341	+	3.48389i	−1.75800	+	0.179429i
$378$		0			0
$379$	0.520109	+	1.94107i	0.0267162	+	0.0997062i	0.977997	−	0.208621i	$-0.0668975\pi$
$379$	0.520109	+	1.94107i	0.0267162	+	0.0997062i	−0.951280	+	0.308327i	$0.900231\pi$
$380$	19.8980	−	8.16377i	1.02074	−	0.418792i
$381$		0			0
$382$			2.56386i			0.131179i
$383$	−13.2258	−	22.9077i	−0.675806	−	1.17053i	−0.976233	−	0.216725i	$-0.930462\pi$
$383$	−13.2258	−	22.9077i	−0.675806	−	1.17053i	0.300427	−	0.953805i	$-0.402871\pi$
$384$		0			0
$385$	−4.47235	−	3.45570i	−0.227932	−	0.176119i
$386$	−2.49457	−	4.32072i	−0.126970	−	0.219919i
$387$		0			0
$388$	−10.7577	−	6.21098i	−0.546141	−	0.315315i
$389$	0.650094			0.0329611			0.0164805	−	0.999864i	$-0.494754\pi$
$389$	0.650094			0.0329611			0.0164805	+	0.999864i	$0.494754\pi$
$390$		0			0
$391$	3.21568			0.162624
$392$	10.4577	+	6.03773i	0.528191	+	0.304951i
$393$		0			0
$394$	3.22615	+	5.58786i	0.162531	+	0.281512i
$395$	−6.92317	+	0.887791i	−0.348343	+	0.0446696i
$396$		0			0
$397$	13.5041	+	23.3897i	0.677750	+	1.17390i	0.975657	+	0.219303i	$0.0703782\pi$
$397$	13.5041	+	23.3897i	0.677750	+	1.17390i	−0.297907	+	0.954595i	$0.596288\pi$
$398$		−	3.87719i		−	0.194346i
$399$		0			0
$400$	3.44350	−	12.5142i	0.172175	−	0.625712i
$401$	1.28339	+	4.78969i	0.0640896	+	0.239186i	0.990539	−	0.137235i	$-0.0438215\pi$
$401$	1.28339	+	4.78969i	0.0640896	+	0.239186i	−0.926449	+	0.376421i	$0.877155\pi$
$402$		0			0
$403$	−24.2426	−	3.91442i	−1.20761	−	0.194991i
$404$			26.2876i			1.30786i
$405$		0			0
$406$	−8.63761	+	14.9608i	−0.428677	+	0.742491i
$407$	−1.21906	−	0.326647i	−0.0604268	−	0.0161913i
$408$		0			0
$409$	5.83965	+	1.56473i	0.288752	+	0.0773708i	0.400288	−	0.916390i	$-0.368910\pi$
$409$	5.83965	+	1.56473i	0.288752	+	0.0773708i	−0.111536	+	0.993760i	$0.535577\pi$
$410$	−0.0818784	+	0.606177i	−0.00404368	+	0.0299370i
$411$		0			0
$412$	−2.04303	+	7.62468i	−0.100653	+	0.375641i
$413$	36.9416	−	9.89848i	1.81778	−	0.487073i
$414$		0			0
$415$	−0.608410	−	4.74450i	−0.0298657	−	0.232898i
$416$	7.37076	−	16.4219i	0.361381	−	0.805150i
$417$		0			0
$418$	−0.930187	+	1.61113i	−0.0454969	+	0.0788030i
$419$	−4.65114	−	2.68534i	−0.227223	−	0.131187i	0.382067	−	0.924135i	$-0.375212\pi$
$419$	−4.65114	−	2.68534i	−0.227223	−	0.131187i	−0.609290	+	0.792947i	$0.708546\pi$
$420$		0			0
$421$	14.1377	+	14.1377i	0.689029	+	0.689029i	0.962017	−	0.272988i	$-0.0880119\pi$
$421$	14.1377	+	14.1377i	0.689029	+	0.689029i	−0.272988	+	0.962017i	$0.588012\pi$
$422$	−5.31418	+	3.06814i	−0.258690	+	0.149355i
$423$		0			0
$424$	−4.58760	−	4.58760i	−0.222794	−	0.222794i
$425$	11.8722	+	0.0798070i	0.575887	+	0.00387121i
$426$		0			0
$427$	11.3905	−	19.7289i	0.551225	−	0.954750i
$428$	18.9395	+	18.9395i	0.915476	+	0.915476i
$429$		0			0
$430$	−1.89349	−	1.46306i	−0.0913122	−	0.0705552i
$431$	−16.1219	+	4.31985i	−0.776564	+	0.208080i	−0.625269	−	0.780409i	$-0.715011\pi$
$431$	−16.1219	+	4.31985i	−0.776564	+	0.208080i	−0.151295	+	0.988489i	$0.548344\pi$
$432$		0			0
$433$	−1.96538	+	7.33490i	−0.0944502	+	0.352493i	−0.996936	−	0.0782277i	$-0.975074\pi$
$433$	−1.96538	+	7.33490i	−0.0944502	+	0.352493i	0.902485	+	0.430721i	$0.141741\pi$
$434$	−8.74255	+	8.74255i	−0.419656	+	0.419656i
$435$		0			0
$436$	−5.41899	−	1.45201i	−0.259522	−	0.0695388i
$437$	−7.41767			−0.354835
$438$		0			0
$439$	6.84536	−	11.8565i	0.326711	−	0.565880i	−0.655146	−	0.755502i	$-0.727393\pi$
$439$	6.84536	−	11.8565i	0.326711	−	0.565880i	0.981857	+	0.189622i	$0.0607262\pi$
$440$	1.08280	+	2.63917i	0.0516206	+	0.125818i
$441$		0			0
$442$	4.17441	+	0.674036i	0.198556	+	0.0320606i
$443$	−6.46290	+	6.46290i	−0.307062	+	0.307062i	−0.843769	−	0.536707i	$-0.819668\pi$
$443$	−6.46290	+	6.46290i	−0.307062	+	0.307062i	0.536707	+	0.843769i	$0.319668\pi$
$444$		0			0
$445$	−2.86680	−	6.98740i	−0.135899	−	0.331235i
$446$	−4.25377	+	2.45591i	−0.201422	+	0.116291i
$447$		0			0
$448$	5.00971	+	8.67708i	0.236687	+	0.409953i
$449$	6.65458	−	24.8352i	0.314049	−	1.17205i	−0.610822	−	0.791768i	$-0.709161\pi$
$449$	6.65458	−	24.8352i	0.314049	−	1.17205i	0.924872	−	0.380280i	$-0.124172\pi$
$450$		0			0
$451$	0.190442	+	0.329855i	0.00896755	+	0.0155323i
$452$	−7.53143	−	28.1077i	−0.354249	−	1.32207i
$453$		0			0
$454$	−7.21383			−0.338562
$455$	8.59693	−	28.3583i	0.403030	−	1.32946i
$456$		0			0
$457$	−0.716665	−	0.413767i	−0.0335242	−	0.0193552i	0.483144	−	0.875541i	$-0.339495\pi$
$457$	−0.716665	−	0.413767i	−0.0335242	−	0.0193552i	−0.516668	+	0.856186i	$0.672828\pi$
$458$	2.82349	+	10.5374i	0.131933	+	0.492381i
$459$		0			0
$460$	−3.25138	+	4.20792i	−0.151596	+	0.196195i
$461$	−6.23219	+	23.2589i	−0.290262	+	1.08327i	0.654646	+	0.755936i	$0.272818\pi$
$461$	−6.23219	+	23.2589i	−0.290262	+	1.08327i	−0.944908	+	0.327337i	$0.893849\pi$
$462$		0			0
$463$		−	6.35566i		−	0.295373i	−0.989034	−	0.147686i	$-0.952817\pi$
$463$		−	6.35566i		−	0.295373i	0.989034	−	0.147686i	$-0.0471826\pi$
$464$	−21.3935	+	12.3515i	−0.993167	+	0.573405i
$465$		0			0
$466$	−2.99418	−	11.1744i	−0.138703	−	0.517645i
$467$	15.6194	−	15.6194i	0.722781	−	0.722781i	−0.246390	−	0.969171i	$-0.579244\pi$
$467$	15.6194	−	15.6194i	0.722781	−	0.722781i	0.969171	+	0.246390i	$0.0792443\pi$
$468$		0			0
$469$		−	45.0153i		−	2.07861i
$470$	−1.62295	+	3.88119i	−0.0748610	+	0.179026i
$471$		0			0
$472$	−18.6455	−	4.99605i	−0.858229	−	0.229962i
$473$	−1.49000			−0.0685104
$474$		0			0
$475$	−27.3859	−	0.184093i	−1.25655	−	0.00844675i
$476$	−10.8371	+	10.8371i	−0.496716	+	0.496716i
$477$		0			0
$478$	9.85182	−	2.63979i	0.450612	−	0.120741i
$479$	−9.14111	+	2.44935i	−0.417668	+	0.111914i	−0.461532	−	0.887124i	$-0.652700\pi$
$479$	−9.14111	+	2.44935i	−0.417668	+	0.111914i	0.0438638	+	0.999038i	$0.486033\pi$
$480$		0			0
$481$	−0.671874	−	6.58282i	−0.0306348	−	0.300151i
$482$	1.08228	+	1.08228i	0.0492964	+	0.0492964i
$483$		0			0
$484$	−16.0095	−	9.24310i	−0.727705	−	0.420141i
$485$	9.58681	+	12.5811i	0.435314	+	0.571278i
$486$		0			0
$487$	5.33382	−	3.07948i	0.241698	−	0.139545i	−0.374259	−	0.927324i	$-0.622103\pi$
$487$	5.33382	−	3.07948i	0.241698	−	0.139545i	0.615957	+	0.787780i	$0.288769\pi$
$488$	−9.95775	+	5.74911i	−0.450766	+	0.260250i
$489$		0			0
$490$	−4.35707	−	5.71793i	−0.196832	−	0.258310i
$491$	−12.8290	−	7.40681i	−0.578964	−	0.334265i	0.181758	−	0.983343i	$-0.441821\pi$
$491$	−12.8290	−	7.40681i	−0.578964	−	0.334265i	−0.760721	+	0.649078i	$0.775155\pi$
$492$		0			0
$493$	−15.9781	−	15.9781i	−0.719615	−	0.719615i
$494$	−9.62921	−	1.55481i	−0.433238	−	0.0699544i
$495$		0			0
$496$	−17.0775	+	4.57590i	−0.766802	+	0.205464i
$497$	23.7993	−	6.37699i	1.06754	−	0.286047i
$498$		0			0
$499$	21.0529	−	21.0529i	0.942459	−	0.942459i	−0.0559733	−	0.998432i	$-0.517826\pi$
$499$	21.0529	−	21.0529i	0.942459	−	0.942459i	0.998432	+	0.0559733i	$0.0178262\pi$
$500$	−12.1085	+	15.4549i	−0.541508	+	0.691164i
$501$		0			0
$502$	14.5844			0.650933
$503$	−37.4393	−	10.0318i	−1.66934	−	0.447297i	−0.704404	−	0.709799i	$-0.748786\pi$
$503$	−37.4393	−	10.0318i	−1.66934	−	0.447297i	−0.964932	+	0.262502i	$0.915452\pi$
$504$		0			0
$505$	12.9135	−	30.8820i	0.574643	−	1.37423i
$506$		−	0.459974i		−	0.0204484i
$507$		0			0
$508$	−10.3059	+	10.3059i	−0.457250	+	0.457250i
$509$	1.43699	+	5.36291i	0.0636933	+	0.237707i	0.990432	−	0.137999i	$-0.0440670\pi$
$509$	1.43699	+	5.36291i	0.0636933	+	0.237707i	−0.926739	+	0.375706i	$0.877400\pi$
$510$		0			0
$511$	10.7474	−	6.20501i	0.475437	−	0.274493i
$512$		−	22.5909i		−	0.998384i
$513$		0			0
$514$	−0.915926	+	3.41828i	−0.0403997	+	0.150774i
$515$	6.14563	−	7.95364i	0.270809	−	0.350479i
$516$		0			0
$517$	0.677985	+	2.53028i	0.0298178	+	0.111281i
$518$	−2.88521	−	1.66578i	−0.126769	−	0.0731900i
$519$		0			0
$520$	−10.9144	+	10.2261i	−0.478628	+	0.448443i
$521$	13.8692			0.607619			0.303809	−	0.952733i	$-0.401741\pi$
$521$	13.8692			0.607619			0.303809	+	0.952733i	$0.401741\pi$
$522$		0			0
$523$	8.10818	+	30.2601i	0.354546	+	1.32318i	0.881055	+	0.473014i	$0.156834\pi$
$523$	8.10818	+	30.2601i	0.354546	+	1.32318i	−0.526509	+	0.850170i	$0.676499\pi$
$524$	1.20649	+	2.08970i	0.0527057	+	0.0912890i
$525$		0			0
$526$	−1.72130	+	6.42400i	−0.0750524	+	0.280100i
$527$	−8.08609	−	14.0055i	−0.352236	−	0.610090i
$528$		0			0
$529$	−18.3303	+	10.5830i	−0.796969	+	0.460130i
$530$	1.46606	+	3.57331i	0.0636816	+	0.155214i
$531$		0			0
$532$	24.9981	−	24.9981i	1.08381	−	1.08381i
$533$	−1.26140	+	1.54815i	−0.0546371	+	0.0670579i
$534$		0			0
$535$	−12.9458	−	31.5534i	−0.559695	−	1.36417i
$536$	−11.3602	+	19.6765i	−0.490688	+	0.849897i
$537$		0			0
$538$	4.00246			0.172558
$539$	−4.32381	−	1.15856i	−0.186240	−	0.0499028i
$540$		0			0
$541$	−10.7732	+	10.7732i	−0.463175	+	0.463175i	−0.899695	−	0.436520i	$-0.856211\pi$
$541$	−10.7732	+	10.7732i	−0.463175	+	0.463175i	0.436520	+	0.899695i	$0.356211\pi$
$542$	1.17561	−	4.38745i	0.0504969	−	0.188457i
$543$		0			0
$544$	11.4504	−	3.06813i	0.490932	−	0.131545i
$545$	5.65278	+	4.36780i	0.242139	+	0.187096i
$546$		0			0
$547$	14.2704	+	14.2704i	0.610159	+	0.610159i	0.942987	−	0.332828i	$-0.108003\pi$
$547$	14.2704	+	14.2704i	0.610159	+	0.610159i	−0.332828	+	0.942987i	$0.608003\pi$
$548$	10.8240	−	18.7477i	0.462379	−	0.800863i
$549$		0			0
$550$	0.0114157	−	1.69822i	0.000486767	−	0.0724122i
$551$	36.8569	+	36.8569i	1.57016	+	1.57016i
$552$		0			0
$553$	−9.93592	+	5.73651i	−0.422518	+	0.243941i
$554$	9.02605	+	9.02605i	0.383480	+	0.383480i
$555$		0			0
$556$	−9.73546	−	5.62077i	−0.412875	−	0.238374i
$557$	8.35584	−	14.4727i	0.354048	−	0.613229i	−0.632906	−	0.774228i	$-0.718138\pi$
$557$	8.35584	−	14.4727i	0.354048	−	0.613229i	0.986955	+	0.160999i	$0.0514716\pi$
$558$		0			0
$559$	−2.77765	−	7.30159i	−0.117482	−	0.308824i
$560$	−2.71361	−	21.1613i	−0.114671	−	0.894227i
$561$		0			0
$562$	−3.65629	+	0.979701i	−0.154231	+	0.0413262i
$563$	5.84179	−	21.8019i	0.246202	−	0.918839i	−0.726573	−	0.687089i	$-0.758888\pi$
$563$	5.84179	−	21.8019i	0.246202	−	0.918839i	0.972775	−	0.231750i	$-0.0744452\pi$
$564$		0			0
$565$	−4.95987	+	36.7198i	−0.208663	+	1.54481i
$566$	4.19136	+	1.12307i	0.176176	+	0.0472063i
$567$		0			0
$568$	−12.0122	−	3.21865i	−0.504019	−	0.135052i
$569$	−2.86843	+	4.96826i	−0.120251	+	0.208280i	−0.919866	−	0.392232i	$-0.871703\pi$
$569$	−2.86843	+	4.96826i	−0.120251	+	0.208280i	0.799616	+	0.600512i	$0.205037\pi$
$570$		0			0
$571$			46.5634i			1.94862i	0.225214	+	0.974309i	$0.427692\pi$
$571$			46.5634i			1.94862i	−0.225214	+	0.974309i	$0.572308\pi$
$572$	−0.694069	+	4.29848i	−0.0290205	+	0.179728i
$573$		0			0
$574$	0.260227	+	0.971181i	0.0108617	+	0.0405363i
$575$	5.88672	−	3.34614i	0.245493	−	0.139544i
$576$		0			0
$577$		−	28.9429i		−	1.20491i	−0.798153	−	0.602455i	$-0.794189\pi$
$577$		−	28.9429i		−	1.20491i	0.798153	−	0.602455i	$-0.205811\pi$
$578$	−2.80580	−	4.85978i	−0.116706	−	0.202140i
$579$		0			0
$580$	37.0638	−	4.75287i	1.53899	−	0.197352i
$581$	−3.93127	−	6.80916i	−0.163097	−	0.282491i
$582$		0			0
$583$	2.08281	+	1.20251i	0.0862613	+	0.0498030i
$584$	−6.26369			−0.259193
$585$		0			0
$586$	−6.53726			−0.270052
$587$	−17.0534	−	9.84577i	−0.703868	−	0.406379i	0.104918	−	0.994481i	$-0.466542\pi$
$587$	−17.0534	−	9.84577i	−0.703868	−	0.406379i	−0.808787	+	0.588102i	$0.799875\pi$
$588$		0			0
$589$	18.6524	+	32.3069i	0.768558	+	1.33118i
$590$	9.09338	+	7.02628i	0.374368	+	0.289267i
$591$		0			0
$592$	−2.38201	−	4.12577i	−0.0979001	−	0.169568i
$593$		−	21.8216i		−	0.896106i	−0.894007	−	0.448053i	$-0.852118\pi$
$593$		−	21.8216i		−	0.896106i	0.894007	−	0.448053i	$-0.147882\pi$
$594$		0			0
$595$	18.0547	−	7.40749i	0.740169	−	0.303677i
$596$	−7.63679	−	28.5009i	−0.312815	−	1.16744i
$597$		0			0
$598$	2.25405	−	0.857481i	0.0921750	−	0.0350650i
$599$		−	37.6041i		−	1.53646i	−0.640172	−	0.768232i	$-0.721137\pi$
$599$		−	37.6041i		−	1.53646i	0.640172	−	0.768232i	$-0.278863\pi$
$600$		0			0
$601$	10.1487	−	17.5781i	0.413976	−	0.717027i	−0.581344	−	0.813658i	$-0.697473\pi$
$601$	10.1487	−	17.5781i	0.413976	−	0.717027i	0.995320	+	0.0966302i	$0.0308064\pi$
$602$	−3.79922	−	1.01800i	−0.154845	−	0.0414905i
$603$		0			0
$604$	7.95310	+	2.13103i	0.323607	+	0.0867103i
$605$	14.2670	+	18.7230i	0.580034	+	0.761199i
$606$		0			0
$607$	8.91757	−	33.2808i	0.361953	−	1.35083i	−0.509552	−	0.860440i	$-0.670189\pi$
$607$	8.91757	−	33.2808i	0.361953	−	1.35083i	0.871505	−	0.490387i	$-0.163144\pi$
$608$	−26.4129	+	7.07732i	−1.07119	+	0.287023i
$609$		0			0
$610$	6.78955	−	0.870657i	0.274901	−	0.0352519i
$611$	−11.1354	+	8.03931i	−0.450491	+	0.325236i
$612$		0			0
$613$	12.4332	−	21.5350i	0.502173	−	0.869790i	−0.497824	−	0.867278i	$-0.665867\pi$
$613$	12.4332	−	21.5350i	0.502173	−	0.869790i	0.999997	−	0.00251133i	$-0.000799381\pi$
$614$	−6.62053	−	3.82236i	−0.267183	−	0.154258i
$615$		0			0
$616$	3.31563	+	3.31563i	0.133591	+	0.133591i
$617$	24.0895	−	13.9081i	0.969805	−	0.559917i	0.0706286	−	0.997503i	$-0.477499\pi$
$617$	24.0895	−	13.9081i	0.969805	−	0.559917i	0.899177	+	0.437585i	$0.144166\pi$
$618$		0			0
$619$	−19.5593	−	19.5593i	−0.786156	−	0.786156i	0.194705	−	0.980862i	$-0.437625\pi$
$619$	−19.5593	−	19.5593i	−0.786156	−	0.786156i	−0.980862	+	0.194705i	$0.937625\pi$
$620$	26.5030	+	3.57985i	1.06439	+	0.143770i
$621$		0			0
$622$	−1.32099	+	2.28803i	−0.0529671	+	0.0917416i
$623$	−8.77838	−	8.77838i	−0.351698	−	0.351698i
$624$		0			0
$625$	21.8167	−	12.2078i	0.872669	−	0.488312i
$626$	16.4570	−	4.40965i	0.657755	−	0.176245i
$627$		0			0
$628$	6.35012	−	23.6990i	0.253397	−	0.945692i
$629$	3.08139	−	3.08139i	0.122863	−	0.122863i
$630$		0			0
$631$	12.6187	+	3.38116i	0.502341	+	0.134602i	0.501086	−	0.865397i	$-0.332934\pi$
$631$	12.6187	+	3.38116i	0.502341	+	0.134602i	0.00125496	+	0.999999i	$0.499601\pi$
$632$	5.79076			0.230344
$633$		0			0
$634$	−4.68840	+	8.12054i	−0.186200	+	0.322508i
$635$	17.1697	−	7.04442i	0.681360	−	0.279549i
$636$		0			0
$637$	−2.38302	−	23.3481i	−0.0944186	−	0.925086i
$638$	−2.28552	+	2.28552i	−0.0904846	+	0.0904846i
$639$		0			0
$640$	−9.77471	+	23.3757i	−0.386379	+	0.924006i
$641$	−23.7092	+	13.6885i	−0.936456	+	0.540663i	−0.888848	−	0.458203i	$-0.848493\pi$
$641$	−23.7092	+	13.6885i	−0.936456	+	0.540663i	−0.0476083	+	0.998866i	$0.515160\pi$
$642$		0			0
$643$	−15.7510	−	27.2816i	−0.621161	−	1.07588i	−0.989270	−	0.146099i	$-0.953328\pi$
$643$	−15.7510	−	27.2816i	−0.621161	−	1.07588i	0.368109	−	0.929783i	$-0.380005\pi$
$644$	−2.26231	+	8.44305i	−0.0891475	+	0.332703i
$645$		0			0
$646$	−3.21181	−	5.56301i	−0.126367	−	0.218874i
$647$	10.8106	+	40.3457i	0.425008	+	1.58615i	0.763905	+	0.645329i	$0.223280\pi$
$647$	10.8106	+	40.3457i	0.425008	+	1.58615i	−0.338896	+	0.940824i	$0.610054\pi$
$648$		0			0
$649$	7.15565			0.280884
$650$	8.34320	−	3.10986i	0.327247	−	0.121979i
$651$		0			0
$652$	0.200698	+	0.115873i	0.00785996	+	0.00453795i
$653$	3.93069	+	14.6695i	0.153820	+	0.574064i	0.999204	+	0.0399041i	$0.0127052\pi$
$653$	3.93069	+	14.6695i	0.153820	+	0.574064i	−0.845384	+	0.534160i	$0.820628\pi$
$654$		0			0
$655$	−0.390807	−	3.04759i	−0.0152701	−	0.119079i
$656$	−0.372117	+	1.38876i	−0.0145287	+	0.0542220i
$657$		0			0
$658$			6.91493i			0.269572i
$659$	24.6914	−	14.2556i	0.961840	−	0.555319i	0.0651015	−	0.997879i	$-0.479263\pi$
$659$	24.6914	−	14.2556i	0.961840	−	0.555319i	0.896739	+	0.442560i	$0.145930\pi$
$660$		0			0
$661$	−1.63091	−	6.08664i	−0.0634351	−	0.236743i	0.926928	−	0.375240i	$-0.122440\pi$
$661$	−1.63091	−	6.08664i	−0.0634351	−	0.236743i	−0.990363	+	0.138497i	$0.955773\pi$
$662$	−2.45054	+	2.45054i	−0.0952430	+	0.0952430i
$663$		0			0
$664$			3.96845i			0.154006i
$665$	−41.6471	+	17.0870i	−1.61501	+	0.662606i
$666$		0			0
$667$	−12.4483	−	3.33552i	−0.482002	−	0.129152i
$668$	−37.9955			−1.47009
$669$		0			0
$670$	10.7585	−	8.19801i	0.415638	−	0.316717i
$671$	3.01394	−	3.01394i	0.116352	−	0.116352i
$672$		0			0
$673$	−22.1285	+	5.92931i	−0.852991	+	0.228558i	−0.658719	−	0.752389i	$-0.728901\pi$
$673$	−22.1285	+	5.92931i	−0.852991	+	0.228558i	−0.194272	+	0.980948i	$0.562235\pi$
$674$	−0.743468	+	0.199212i	−0.0286373	+	0.00767334i
$675$		0			0
$676$	−22.3581	+	4.61199i	−0.859926	+	0.177384i
$677$	16.1247	+	16.1247i	0.619724	+	0.619724i	0.945461	−	0.325736i	$-0.105612\pi$
$677$	16.1247	+	16.1247i	0.619724	+	0.619724i	−0.325736	+	0.945461i	$0.605612\pi$
$678$		0			0
$679$	22.5163	+	12.9998i	0.864096	+	0.498886i
$680$	−9.76121	−	1.31848i	−0.374325	−	0.0505614i
$681$		0			0
$682$	−2.00337	+	1.15664i	−0.0767129	+	0.0442902i
$683$	−27.7544	+	16.0240i	−1.06199	+	0.613142i	−0.925983	−	0.377565i	$-0.876761\pi$
$683$	−27.7544	+	16.0240i	−1.06199	+	0.613142i	−0.136010	+	0.990707i	$0.543428\pi$
$684$		0			0
$685$	−21.9253	+	16.7071i	−0.837724	+	0.638346i
$686$	0.771532	+	0.445444i	0.0294572	+	0.0170071i
$687$		0			0
$688$	−3.97707	−	3.97707i	−0.151624	−	0.151624i
$689$	−2.01001	+	12.4483i	−0.0765753	+	0.474243i
$690$		0			0
$691$	−0.532264	+	0.142620i	−0.0202483	+	0.00542551i	−0.268929	−	0.963160i	$-0.586670\pi$
$691$	−0.532264	+	0.142620i	−0.0202483	+	0.00542551i	0.248681	+	0.968586i	$0.420003\pi$
$692$	−13.1180	+	3.51496i	−0.498672	+	0.133619i
$693$		0			0
$694$	−9.02132	+	9.02132i	−0.342445	+	0.342445i
$695$	8.67580	+	11.3855i	0.329092	+	0.431878i
$696$		0			0
$697$	−1.31514			−0.0498144
$698$	−4.48442	−	1.20160i	−0.169738	−	0.0454811i
$699$		0			0
$700$	−8.56194	+	31.1155i	−0.323611	+	1.17605i
$701$			9.52279i			0.359671i	0.983697	+	0.179835i	$0.0575565\pi$
$701$			9.52279i			0.359671i	−0.983697	+	0.179835i	$0.942443\pi$
$702$		0			0
$703$	−7.10792	+	7.10792i	−0.268080	+	0.268080i
$704$	0.485195	+	1.81077i	0.0182865	+	0.0682460i
$705$		0			0
$706$	−1.39674	+	0.806411i	−0.0525672	+	0.0303497i
$707$		−	55.0209i		−	2.06927i
$708$		0			0
$709$	8.39944	−	31.3471i	0.315448	−	1.17727i	−0.608124	−	0.793842i	$-0.708078\pi$
$709$	8.39944	−	31.3471i	0.315448	−	1.17727i	0.923572	−	0.383425i	$-0.125255\pi$
$710$	5.85831	+	4.52661i	0.219859	+	0.169881i
$711$		0			0
$712$	1.62175	+	6.05244i	0.0607776	+	0.226825i
$713$	−7.98782	−	4.61177i	−0.299146	−	0.172712i
$714$		0			0
$715$	2.92695	−	4.70877i	0.109462	−	0.176098i
$716$	28.7180			1.07324
$717$		0			0
$718$	−0.564197	−	2.10561i	−0.0210557	−	0.0785808i
$719$	−4.21240	−	7.29608i	−0.157096	−	0.272098i	0.776724	−	0.629841i	$-0.216880\pi$
$719$	−4.21240	−	7.29608i	−0.157096	−	0.272098i	−0.933820	+	0.357743i	$0.883546\pi$
$720$		0			0
$721$	4.27612	−	15.9587i	0.159251	−	0.594333i
$722$	2.71668	+	4.70543i	0.101104	+	0.175118i
$723$		0			0
$724$	−27.4332	+	15.8385i	−1.01955	+	0.588635i
$725$	−45.8763	−	12.6236i	−1.70380	−	0.468830i
$726$		0			0
$727$	−8.33682	+	8.33682i	−0.309195	+	0.309195i	−0.844597	−	0.535402i	$-0.820160\pi$
$727$	−8.33682	+	8.33682i	−0.309195	+	0.309195i	0.535402	+	0.844597i	$0.320160\pi$
$728$	−10.0669	+	22.4288i	−0.373104	+	0.831268i
$729$		0			0
$730$	3.44025	+	1.43857i	0.127329	+	0.0532437i
$731$	2.57239	−	4.45551i	0.0951432	−	0.164793i
$732$		0			0
$733$	−18.6238			−0.687887			−0.343944	−	0.938990i	$-0.611763\pi$
$733$	−18.6238			−0.687887			−0.343944	+	0.938990i	$0.611763\pi$
$734$	−11.9696	−	3.20725i	−0.441807	−	0.118382i
$735$		0			0
$736$	4.78070	−	4.78070i	0.176219	−	0.176219i
$737$	2.17988	−	8.13543i	0.0802970	−	0.299672i
$738$		0			0
$739$	−31.8740	+	8.54061i	−1.17250	+	0.314171i	−0.791949	−	0.610587i	$-0.790934\pi$
$739$	−31.8740	+	8.54061i	−1.17250	+	0.314171i	−0.380555	+	0.924758i	$0.624267\pi$
$740$	0.916598	+	7.14782i	0.0336948	+	0.262759i
$741$		0			0
$742$	4.48920	+	4.48920i	0.164804	+	0.164804i
$743$	18.7850	−	32.5366i	0.689155	−	1.19365i	−0.282957	−	0.959133i	$-0.591315\pi$
$743$	18.7850	−	32.5366i	0.689155	−	1.19365i	0.972112	−	0.234518i	$-0.0753512\pi$
$744$		0			0
$745$	−5.02925	+	37.2335i	−0.184258	+	1.36413i
$746$	3.99061	+	3.99061i	0.146107	+	0.146107i
$747$		0			0
$748$	−2.48333	+	1.43375i	−0.0907995	+	0.0524231i
$749$	−39.6410	−	39.6410i	−1.44845	−	1.44845i
$750$		0			0
$751$	−29.1051	−	16.8038i	−1.06206	−	0.613181i	−0.136059	−	0.990701i	$-0.543444\pi$
$751$	−29.1051	−	16.8038i	−1.06206	−	0.613181i	−0.926001	+	0.377520i	$0.876777\pi$
$752$	−4.94407	+	8.56339i	−0.180292	+	0.312275i
$753$		0			0
$754$	−15.4606	−	6.93928i	−0.563041	−	0.252714i
$755$	−8.29623	−	6.41034i	−0.301931	−	0.233296i
$756$		0			0
$757$	15.5871	−	4.17654i	0.566521	−	0.151799i	0.0358205	−	0.999358i	$-0.488596\pi$
$757$	15.5871	−	4.17654i	0.566521	−	0.151799i	0.530701	+	0.847559i	$0.321929\pi$
$758$	−0.256883	+	0.958699i	−0.00933040	+	0.0348215i
$759$		0			0
$760$	22.5164	+	3.04137i	0.816756	+	0.110322i
$761$	15.1340	+	4.05514i	0.548606	+	0.146999i	0.522467	−	0.852660i	$-0.325012\pi$
$761$	15.1340	+	4.05514i	0.548606	+	0.146999i	0.0261397	+	0.999658i	$0.491679\pi$
$762$		0			0
$763$	11.3421	+	3.03911i	0.410612	+	0.110023i
$764$	4.55789	−	7.89449i	0.164899	−	0.285613i
$765$		0			0
$766$		−	13.0645i		−	0.472039i
$767$	13.3395	+	35.0655i	0.481662	+	1.26614i
$768$		0			0
$769$	8.43930	+	31.4959i	0.304329	+	1.13577i	0.933522	+	0.358521i	$0.116719\pi$
$769$	8.43930	+	31.4959i	0.304329	+	1.13577i	−0.629193	+	0.777249i	$0.716614\pi$
$770$	−1.05958	−	2.58256i	−0.0381845	−	0.0930690i
$771$		0			0
$772$			17.7388i			0.638433i
$773$	11.9531	+	20.7033i	0.429921	+	0.744646i	0.996866	−	0.0791103i	$-0.0252079\pi$
$773$	11.9531	+	20.7033i	0.429921	+	0.744646i	−0.566944	+	0.823756i	$0.691875\pi$
$774$		0			0
$775$	−29.3764	−	17.2248i	−1.05523	−	0.618733i
$776$	−6.56136	−	11.3646i	−0.235539	−	0.407966i
$777$		0			0
$778$	0.278066	+	0.160541i	0.00996914	+	0.00575569i
$779$	3.03366			0.108692
$780$		0			0
$781$	4.60995			0.164957
$782$	1.37545	+	0.794114i	0.0491858	+	0.0283975i
$783$		0			0
$784$	−8.44858	−	14.6334i	−0.301735	−	0.522620i
$785$	−19.1018	+	24.7214i	−0.681772	+	0.882346i
$786$		0			0
$787$	−7.85572	−	13.6065i	−0.280026	−	0.485020i	0.691365	−	0.722506i	$-0.257010\pi$
$787$	−7.85572	−	13.6065i	−0.280026	−	0.485020i	−0.971391	+	0.237486i	$0.923676\pi$
$788$		−	22.9411i		−	0.817242i
$789$		0			0
$790$	−3.18050	−	1.32995i	−0.113157	−	0.0473174i
$791$	15.7635	+	58.8303i	0.560487	+	2.09176i
$792$		0			0
$793$	20.3880	+	9.15090i	0.724000	+	0.324958i
$794$			13.3394i			0.473397i
$795$		0			0
$796$	−6.89264	+	11.9384i	−0.244303	+	0.423146i
$797$	30.1666	+	8.08312i	1.06856	+	0.286319i	0.749900	−	0.661552i	$-0.230102\pi$
$797$	30.1666	+	8.08312i	1.06856	+	0.286319i	0.318656	+	0.947870i	$0.396768\pi$
$798$		0			0
$799$	−8.73669	−	2.34099i	−0.309082	−	0.0828183i
$800$	17.7689	−	17.5316i	0.628225	−	0.619836i
$801$		0			0
$802$	−0.633871	+	2.36564i	−0.0223827	+	0.0835336i
$803$	2.24281	−	0.600960i	0.0791471	−	0.0212074i
$804$		0			0
$805$	6.80525	−	8.80732i	0.239853	−	0.310417i
$806$	−9.40267	−	7.66106i	−0.331195	−	0.269849i
$807$		0			0
$808$	−13.8853	+	24.0500i	−0.488483	+	0.846078i
$809$	−11.4546	−	6.61331i	−0.402722	−	0.232512i	0.284936	−	0.958547i	$-0.408028\pi$
$809$	−11.4546	−	6.61331i	−0.402722	−	0.232512i	−0.687658	+	0.726035i	$0.741361\pi$
$810$		0			0
$811$	22.0736	+	22.0736i	0.775109	+	0.775109i	0.978995	−	0.203886i	$-0.0653572\pi$
$811$	22.0736	+	22.0736i	0.775109	+	0.775109i	−0.203886	+	0.978995i	$0.565357\pi$
$812$	53.1928	−	30.7109i	1.86670	−	1.07774i
$813$		0			0
$814$	−0.440767	−	0.440767i	−0.0154489	−	0.0154489i
$815$	−0.178853	−	0.234715i	−0.00626496	−	0.00822172i
$816$		0			0
$817$	−5.93379	+	10.2776i	−0.207597	+	0.359568i
$818$	2.11139	+	2.11139i	0.0738230	+	0.0738230i
$819$		0			0
$820$	1.32974	−	1.72095i	0.0464366	−	0.0600981i
$821$	8.74860	−	2.34418i	0.305328	−	0.0818124i	−0.102902	−	0.994692i	$-0.532813\pi$
$821$	8.74860	−	2.34418i	0.305328	−	0.0818124i	0.408230	+	0.912879i	$0.366146\pi$
$822$		0			0
$823$	10.8551	−	40.5117i	0.378384	−	1.41215i	−0.469953	−	0.882691i	$-0.655729\pi$
$823$	10.8551	−	40.5117i	0.378384	−	1.41215i	0.848337	−	0.529457i	$-0.177604\pi$
$824$	−5.89653	+	5.89653i	−0.205415	+	0.205415i
$825$		0			0
$826$	18.2455	+	4.88888i	0.634844	+	0.170106i
$827$	−38.2009			−1.32838			−0.664188	−	0.747566i	$-0.731222\pi$
$827$	−38.2009			−1.32838			−0.664188	+	0.747566i	$0.731222\pi$
$828$		0			0
$829$	−14.6750	+	25.4178i	−0.509682	+	0.882796i	0.490255	+	0.871579i	$0.336904\pi$
$829$	−14.6750	+	25.4178i	−0.509682	+	0.882796i	−0.999937	+	0.0112165i	$0.996430\pi$
$830$	0.911423	−	2.17962i	0.0316359	−	0.0756557i
$831$		0			0
$832$	−7.96898	+	5.75327i	−0.276275	+	0.199459i
$833$	10.9292	−	10.9292i	0.378673	−	0.378673i
$834$		0			0
$835$	44.6360	+	18.6648i	1.54469	+	0.645923i
$836$	5.72835	−	3.30726i	0.198119	−	0.114384i
$837$		0			0
$838$	−1.32629	−	2.29721i	−0.0458161	−	0.0793557i
$839$	−9.11914	+	34.0331i	−0.314828	+	1.17495i	0.609322	+	0.792923i	$0.291442\pi$
$839$	−9.11914	+	34.0331i	−0.314828	+	1.17495i	−0.924150	+	0.382030i	$0.875225\pi$
$840$		0			0
$841$	30.7798	+	53.3122i	1.06137	+	1.83835i
$842$	2.55582	+	9.53846i	0.0880795	+	0.328717i
$843$		0			0
$844$	21.8175			0.750988
$845$	28.5312	+	5.56512i	0.981503	+	0.191446i
$846$		0			0
$847$	33.5084	+	19.3461i	1.15136	+	0.664740i
$848$	2.34967	+	8.76909i	0.0806880	+	0.301132i
$849$		0			0
$850$	5.05841	+	2.96599i	0.173502	+	0.101733i
$851$	0.643261	−	2.40068i	0.0220507	−	0.0822944i
$852$		0			0
$853$		−	17.6392i		−	0.603954i	−0.953315	−	0.301977i	$-0.902353\pi$
$853$		−	17.6392i		−	0.603954i	0.953315	−	0.301977i	$-0.0976465\pi$
$854$	9.74415	−	5.62579i	0.333438	−	0.192511i
$855$		0			0
$856$	7.32342	+	27.3314i	0.250309	+	0.934167i
$857$	−6.30427	+	6.30427i	−0.215350	+	0.215350i	−0.806535	−	0.591186i	$-0.798660\pi$
$857$	−6.30427	+	6.30427i	−0.215350	+	0.215350i	0.591186	+	0.806535i	$0.298660\pi$
$858$		0			0
$859$			29.2307i			0.997338i	0.866793	+	0.498669i	$0.166178\pi$
$859$			29.2307i			0.997338i	−0.866793	+	0.498669i	$0.833822\pi$
$860$	3.22937	+	7.87112i	0.110121	+	0.268403i
$861$		0			0
$862$	−7.96263	−	2.13358i	−0.271208	−	0.0726701i
$863$	15.7688			0.536775			0.268387	−	0.963311i	$-0.413509\pi$
$863$	15.7688			0.536775			0.268387	+	0.963311i	$0.413509\pi$
$864$		0			0
$865$	17.1373	+	2.31480i	0.582687	+	0.0787054i
$866$	−2.65202	+	2.65202i	−0.0901192	+	0.0901192i
$867$		0			0
$868$	42.4615	−	11.3775i	1.44124	−	0.386179i
$869$	−2.07347	+	0.555585i	−0.0703377	+	0.0188469i
$870$		0			0
$871$	43.9305	−	4.48375i	1.48853	−	0.151926i
$872$	−4.19076	−	4.19076i	−0.141917	−	0.141917i
$873$		0			0
$874$	−3.17277	−	1.83180i	−0.107321	−	0.0619616i
$875$	25.3434	−	32.3476i	0.856764	−	1.09355i
$876$		0			0
$877$	−38.7309	+	22.3613i	−1.30785	+	0.755088i	−0.981737	−	0.190242i	$-0.939073\pi$
$877$	−38.7309	+	22.3613i	−1.30785	+	0.755088i	−0.326114	+	0.945331i	$0.605739\pi$
$878$	5.85595	−	3.38094i	0.197629	−	0.114101i
$879$		0			0
$880$	0.534323	−	3.95580i	0.0180120	−	0.133350i
$881$	18.0323	+	10.4110i	0.607525	+	0.350755i	0.771996	−	0.635627i	$-0.219258\pi$
$881$	18.0323	+	10.4110i	0.607525	+	0.350755i	−0.164471	+	0.986382i	$0.552592\pi$
$882$		0			0
$883$	5.33747	+	5.33747i	0.179620	+	0.179620i	0.791190	−	0.611570i	$-0.209462\pi$
$883$	5.33747	+	5.33747i	0.179620	+	0.179620i	−0.611570	+	0.791190i	$0.709462\pi$
$884$	−11.6553	−	9.49648i	−0.392011	−	0.319401i
$885$		0			0
$886$	−4.36041	+	1.16837i	−0.146491	+	0.0392521i
$887$	−25.8911	+	6.93749i	−0.869337	+	0.232938i	−0.665801	−	0.746129i	$-0.731910\pi$
$887$	−25.8911	+	6.93749i	−0.869337	+	0.232938i	−0.203536	+	0.979067i	$0.565243\pi$
$888$		0			0
$889$	21.5706	−	21.5706i	0.723454	−	0.723454i
$890$	0.499324	−	3.69669i	0.0167374	−	0.123913i
$891$		0			0
$892$	17.4639			0.584736
$893$	20.1531	+	5.40002i	0.674399	+	0.180705i
$894$		0			0
$895$	−33.7370	−	14.1074i	−1.12770	−	0.471557i
$896$			41.6474i			1.39134i
$897$		0			0
$898$	8.97946	−	8.97946i	0.299648	−	0.299648i
$899$	16.7749	+	62.6048i	0.559475	+	2.08799i
$900$		0			0
$901$	−7.19167	+	4.15211i	−0.239589	+	0.138327i
$902$			0.188119i			0.00626368i
$903$		0			0
$904$	7.95630	−	29.6933i	0.264623	−	0.987585i
$905$	40.0082	−	5.13044i	1.32992	−	0.170542i
$906$		0			0
$907$	10.4931	+	39.1608i	0.348418	+	1.30031i	0.888568	+	0.458744i	$0.151701\pi$
$907$	10.4931	+	39.1608i	0.348418	+	1.30031i	−0.540151	+	0.841568i	$0.681633\pi$
$908$	22.2124	+	12.8243i	0.737144	+	0.425590i
$909$		0			0
$910$	10.6803	−	10.0067i	0.354048	−	0.331720i
$911$	−8.00072			−0.265076			−0.132538	−	0.991178i	$-0.542313\pi$
$911$	−8.00072			−0.265076			−0.132538	+	0.991178i	$0.542313\pi$
$912$		0			0
$913$	−0.380746	−	1.42096i	−0.0126009	−	0.0470271i
$914$	−0.204360	−	0.353962i	−0.00675963	−	0.0117080i
$915$		0			0
$916$	10.0389	−	37.4656i	0.331694	−	1.23790i
$917$	−2.52522	−	4.37381i	−0.0833901	−	0.144436i
$918$		0			0
$919$	−1.84237	+	1.06369i	−0.0607741	+	0.0350879i	−0.530079	−	0.847948i	$-0.677838\pi$
$919$	−1.84237	+	1.06369i	−0.0607741	+	0.0350879i	0.469305	+	0.883036i	$0.344504\pi$
$920$	−5.19728	+	2.13235i	−0.171349	+	0.0703014i
$921$		0			0
$922$	−8.40950	+	8.40950i	−0.276952	+	0.276952i
$923$	8.59384	+	22.5905i	0.282870	+	0.743577i
$924$		0			0
$925$	2.43449	−	8.84732i	0.0800455	−	0.290898i
$926$	1.56954	−	2.71852i	0.0515782	−	0.0893360i
$927$		0			0
$928$	−47.5087			−1.55955
$929$	−19.2515	−	5.15841i	−0.631620	−	0.169242i	−0.0712153	−	0.997461i	$-0.522688\pi$
$929$	−19.2515	−	5.15841i	−0.631620	−	0.169242i	−0.560405	+	0.828219i	$0.689354\pi$
$930$		0			0
$931$	−25.2106	+	25.2106i	−0.826243	+	0.826243i
$932$	−10.6458	+	39.7305i	−0.348713	+	1.30142i
$933$		0			0
$934$	10.5382	−	2.82369i	0.344819	−	0.0923940i
$935$	3.62166	−	0.464422i	0.118441	−	0.0151882i
$936$		0			0
$937$	17.2774	+	17.2774i	0.564427	+	0.564427i	0.930562	−	0.366135i	$-0.119319\pi$
$937$	17.2774	+	17.2774i	0.564427	+	0.564427i	−0.366135	+	0.930562i	$0.619319\pi$
$938$	11.1166	−	19.2545i	0.362969	−	0.628680i
$939$		0			0
$940$	11.8970	−	9.06556i	0.388039	−	0.295686i
$941$	−24.2129	−	24.2129i	−0.789319	−	0.789319i	0.192063	−	0.981383i	$-0.438482\pi$
$941$	−24.2129	−	24.2129i	−0.789319	−	0.789319i	−0.981383	+	0.192063i	$0.938482\pi$
$942$		0			0
$943$	−0.649578	+	0.375034i	−0.0211532	+	0.0122128i
$944$	19.0996	+	19.0996i	0.621640	+	0.621640i
$945$		0			0
$946$	−0.637321	−	0.367957i	−0.0207211	−	0.0119633i
$947$	−4.15045	+	7.18880i	−0.134872	+	0.233605i	−0.925548	−	0.378629i	$-0.876396\pi$
$947$	−4.15045	+	7.18880i	−0.134872	+	0.233605i	0.790677	+	0.612234i	$0.209729\pi$
$948$		0			0
$949$	7.12597	+	9.87034i	0.231319	+	0.320405i
$950$	−11.6684	−	6.84172i	−0.378572	−	0.221975i
$951$		0			0
$952$	−15.6388	+	4.19041i	−0.506857	+	0.135812i
$953$	−1.23858	+	4.62244i	−0.0401215	+	0.149736i	−0.983081	−	0.183173i	$-0.941363\pi$
$953$	−1.23858	+	4.62244i	−0.0401215	+	0.149736i	0.942959	+	0.332908i	$0.108030\pi$
$954$		0			0
$955$	−9.23255	+	7.03521i	−0.298758	+	0.227654i
$956$	−35.0280	−	9.38573i	−1.13289	−	0.303556i
$957$		0			0
$958$	−4.51481	−	1.20974i	−0.145867	−	0.0390849i
$959$	−22.6550	+	39.2396i	−0.731568	+	1.26711i
$960$		0			0
$961$			15.3867i			0.496346i
$962$	1.33825	−	2.98160i	0.0431470	−	0.0961306i
$963$		0			0
$964$	−1.40848	−	5.25650i	−0.0453639	−	0.169301i
$965$	8.71398	−	20.8390i	0.280513	−	0.670832i
$966$		0			0
$967$			8.78782i			0.282597i	0.989967	+	0.141299i	$0.0451278\pi$
$967$			8.78782i			0.282597i	−0.989967	+	0.141299i	$0.954872\pi$
$968$	−9.76453	−	16.9127i	−0.313844	−	0.543594i
$969$		0			0
$970$	0.993666	+	7.74880i	0.0319047	+	0.248799i
$971$	−2.71693	−	4.70586i	−0.0871905	−	0.151018i	0.819132	−	0.573605i	$-0.194456\pi$
$971$	−2.71693	−	4.70586i	−0.0871905	−	0.151018i	−0.906323	+	0.422587i	$0.861122\pi$
$972$		0			0
$973$	20.3766	+	11.7645i	0.653245	+	0.377151i
$974$	3.04192			0.0974695
$975$		0			0
$976$	16.0894			0.515010
$977$	−16.1709	−	9.33626i	−0.517352	−	0.298693i	0.218499	−	0.975837i	$-0.429884\pi$
$977$	−16.1709	−	9.33626i	−0.517352	−	0.298693i	−0.735851	+	0.677144i	$0.763217\pi$
$978$		0			0
$979$	−1.16138	−	2.01158i	−0.0371180	−	0.0642903i
$980$	3.25101	+	25.3521i	0.103850	+	0.809842i
$981$		0			0
$982$	−3.65824	−	6.33626i	−0.116739	−	0.202198i
$983$			6.62470i			0.211295i	0.994404	+	0.105648i	$0.0336915\pi$
$983$			6.62470i			0.211295i	−0.994404	+	0.105648i	$0.966308\pi$
$984$		0			0
$985$	−11.2695	+	26.9505i	−0.359077	+	0.858715i
$986$	−2.88852	−	10.7801i	−0.0919893	−	0.343309i
$987$		0			0
$988$	26.8856	+	21.9057i	0.855346	+	0.696915i
$989$		−	2.93424i		−	0.0933033i
$990$		0			0
$991$	21.6135	−	37.4357i	0.686576	−	1.18919i	−0.286362	−	0.958121i	$-0.592446\pi$
$991$	21.6135	−	37.4357i	0.686576	−	1.18919i	0.972939	−	0.231064i	$-0.0742206\pi$
$992$	−32.8433	−	8.80033i	−1.04277	−	0.279411i
$993$		0			0
$994$	11.7545	+	3.14961i	0.372830	+	0.0998995i
$995$	13.9619	−	10.6390i	0.442621	−	0.337278i
$996$		0			0
$997$	11.7001	−	43.6654i	0.370547	−	1.38290i	−0.489197	−	0.872173i	$-0.662710\pi$
$997$	11.7001	−	43.6654i	0.370547	−	1.38290i	0.859744	−	0.510725i	$-0.170623\pi$
$998$	14.2040	−	3.80596i	0.449621	−	0.120476i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.dp.a.397.3		20
3.2	odd	2		65.2.t.a.7.3	yes	20
5.3	odd	4		585.2.cf.a.163.3		20
13.2	odd	12		585.2.cf.a.262.3		20
15.2	even	4		325.2.s.b.293.3		20
15.8	even	4		65.2.o.a.33.3	yes	20
15.14	odd	2		325.2.x.b.7.3		20
39.2	even	12		65.2.o.a.2.3	✓	20
39.5	even	4		845.2.o.e.357.3		20
39.8	even	4		845.2.o.f.357.3		20
39.11	even	12		845.2.o.g.587.3		20
39.17	odd	6		845.2.f.d.437.5		20
39.20	even	12		845.2.k.d.577.5		20
39.23	odd	6		845.2.t.e.427.3		20
39.29	odd	6		845.2.t.f.427.3		20
39.32	even	12		845.2.k.e.577.6		20
39.35	odd	6		845.2.f.e.437.6		20
39.38	odd	2		845.2.t.g.657.3		20
65.28	even	12	inner	585.2.dp.a.28.3		20
195.2	odd	12		325.2.x.b.93.3		20
195.8	odd	4		845.2.t.e.188.3		20
195.23	even	12		845.2.o.f.258.3		20
195.38	even	4		845.2.o.g.488.3		20
195.68	even	12		845.2.o.e.258.3		20
195.83	odd	4		845.2.t.f.188.3		20
195.98	odd	12		845.2.f.d.408.6		20
195.113	even	12		845.2.k.e.268.6		20
195.119	even	12		325.2.s.b.132.3		20
195.128	odd	12		845.2.t.g.418.3		20
195.158	odd	12		65.2.t.a.28.3	yes	20
195.173	even	12		845.2.k.d.268.5		20
195.188	odd	12		845.2.f.e.408.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.3	✓	20	39.2	even	12
65.2.o.a.33.3	yes	20	15.8	even	4
65.2.t.a.7.3	yes	20	3.2	odd	2
65.2.t.a.28.3	yes	20	195.158	odd	12
325.2.s.b.132.3		20	195.119	even	12
325.2.s.b.293.3		20	15.2	even	4
325.2.x.b.7.3		20	15.14	odd	2
325.2.x.b.93.3		20	195.2	odd	12
585.2.cf.a.163.3		20	5.3	odd	4
585.2.cf.a.262.3		20	13.2	odd	12
585.2.dp.a.28.3		20	65.28	even	12	inner
585.2.dp.a.397.3		20	1.1	even	1	trivial
845.2.f.d.408.6		20	195.98	odd	12
845.2.f.d.437.5		20	39.17	odd	6
845.2.f.e.408.5		20	195.188	odd	12
845.2.f.e.437.6		20	39.35	odd	6
845.2.k.d.268.5		20	195.173	even	12
845.2.k.d.577.5		20	39.20	even	12
845.2.k.e.268.6		20	195.113	even	12
845.2.k.e.577.6		20	39.32	even	12
845.2.o.e.258.3		20	195.68	even	12
845.2.o.e.357.3		20	39.5	even	4
845.2.o.f.258.3		20	195.23	even	12
845.2.o.f.357.3		20	39.8	even	4
845.2.o.g.488.3		20	195.38	even	4
845.2.o.g.587.3		20	39.11	even	12
845.2.t.e.188.3		20	195.8	odd	4
845.2.t.e.427.3		20	39.23	odd	6
845.2.t.f.188.3		20	195.83	odd	4
845.2.t.f.427.3		20	39.29	odd	6
845.2.t.g.418.3		20	195.128	odd	12
845.2.t.g.657.3		20	39.38	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.dp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.427732 + 0.246951i) q^{2} +(-0.878030 - 1.52079i) q^{4} +(0.284413 + 2.21791i) q^{5} +(1.83775 + 3.18307i) q^{7} -1.85513i q^{8} +(-0.426062 + 1.01890i) q^{10} +(0.177987 + 0.664257i) q^{11} +(-2.92331 + 2.11051i) q^{13} +1.81533i q^{14} +(-1.29794 + 2.24809i) q^{16} +(-2.29359 - 0.614565i) q^{17} +(5.29067 + 1.41763i) q^{19} +(3.12325 - 2.37992i) q^{20} +(-0.0879082 + 0.328078i) q^{22} +(-1.30811 + 0.350507i) q^{23} +(-4.83822 + 1.26160i) q^{25} +(-1.77158 + 0.180816i) q^{26} +(3.22719 - 5.58966i) q^{28} +(8.24134 + 4.75814i) q^{29} +(4.81595 + 4.81595i) q^{31} +(-4.32351 + 2.49618i) q^{32} +(-0.829273 - 0.829273i) q^{34} +(-6.53707 + 4.98125i) q^{35} +(-0.917615 + 1.58936i) q^{37} +(1.91290 + 1.91290i) q^{38} +(4.11449 - 0.527621i) q^{40} +(0.534988 - 0.143350i) q^{41} +(-0.560778 + 2.09285i) q^{43} +(0.853919 - 0.853919i) q^{44} +(-0.646078 - 0.173116i) q^{46} +3.80918 q^{47} +(-3.25462 + 5.63717i) q^{49} +(-2.38101 - 0.655176i) q^{50} +(5.77640 + 2.59266i) q^{52} +(2.47293 - 2.47293i) q^{53} +(-1.42264 + 0.583682i) q^{55} +(5.90499 - 3.40925i) q^{56} +(2.35005 + 4.07041i) q^{58} +(2.69310 - 10.0508i) q^{59} +(-3.09904 - 5.36770i) q^{61} +(0.870630 + 3.24924i) q^{62} +2.72601 q^{64} +(-5.51234 - 5.88338i) q^{65} +(-10.6066 - 6.12371i) q^{67} +(1.07921 + 4.02768i) q^{68} +(-4.02624 + 0.516303i) q^{70} +(1.73500 - 6.47512i) q^{71} -3.37642i q^{73} +(-0.784986 + 0.453212i) q^{74} +(-2.48945 - 9.29074i) q^{76} +(-1.78728 + 1.78728i) q^{77} +3.12149i q^{79} +(-5.35521 - 2.23932i) q^{80} +(0.264231 + 0.0708006i) q^{82} -2.13918 q^{83} +(0.710723 - 5.26175i) q^{85} +(-0.756694 + 0.756694i) q^{86} +(1.23228 - 0.330188i) q^{88} +(-3.26255 + 0.874198i) q^{89} +(-12.0902 - 5.42653i) q^{91} +(1.68161 + 1.68161i) q^{92} +(1.62931 + 0.940681i) q^{94} +(-1.63944 + 12.1374i) q^{95} +(6.12606 - 3.53688i) q^{97} +(-2.78421 + 1.60746i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} + 6 q^{4} - 2 q^{7} - 2 q^{10} + 16 q^{11} - 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 16 q^{22} + 10 q^{23} + 18 q^{25} + 24 q^{26} + 18 q^{28} - 48 q^{32} + 2 q^{34} - 40 q^{35} - 4 q^{37}+ \cdots + 30 q^{98}+O(q^{100}) \) 20 * q + 6 * q^2 + 6 * q^4 - 2 * q^7 - 2 * q^10 + 16 * q^11 - 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 16 * q^22 + 10 * q^23 + 18 * q^25 + 24 * q^26 + 18 * q^28 - 48 * q^32 + 2 * q^34 - 40 * q^35 - 4 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 + 10 * q^43 + 36 * q^44 + 4 * q^46 + 40 * q^47 + 18 * q^49 - 36 * q^50 - 30 * q^52 + 10 * q^53 - 10 * q^55 + 16 * q^59 - 16 * q^61 + 44 * q^62 + 20 * q^64 + 14 * q^65 + 18 * q^67 - 22 * q^68 - 12 * q^70 + 16 * q^71 - 18 * q^74 - 64 * q^76 + 28 * q^77 + 2 * q^80 + 56 * q^82 - 48 * q^83 - 26 * q^85 - 60 * q^86 + 82 * q^88 + 6 * q^89 + 8 * q^91 + 8 * q^92 - 48 * q^94 + 26 * q^95 + 66 * q^97 + 30 * q^98

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